Joseph J. Biernacki

Tennessee Tech University

Cement Hydration Kinetics and Modeling

About this blog…

This blog was developed as a way to disseminate information about models that have been used, are presently being used to study portland cement hydration (see Hydration Basics). The objective of the blog is to provide detailed information about the theoretical and mathematical origin of each model. The blog is intended for educational and research use and we hope that undergraduate or graduate students learning about cement hydration will find the site useful as well as researchers and engineers at large.  Much of the blog is based on the publications Xie and Biernacki [1] and Biernacki and Xie [2].  A more complete bibliography is also given below.

Our ability to predict hydration behavior is becoming increasingly relevant to the concrete community as modelers begin to link material performance to the dynamics of material properties and chemistry. At early ages, the properties of concrete are changing rapidly due to chemical transformations that effect mechanical, thermal and transport responses of the composite. At later ages, the resulting, nano-, micro-, meso- and macroscopic structure generated by hydration will control the life-cycle performance of the material in the field. Ultimately, creep, shrinkage, chemical and physical durability, and all manner of mechanical response are linked to hydration. As a way to enable the modeling community to better understand hydration, a review of hydration models is presented offering insights into their mathematical origins and relationships one-to-the-other.

The quest for a universal model begins in the 1920’s and continues to the present, and is marked by a number of critical milestones. Unfortunately, the origins and physical interpretation of many of the most commonly used models have been lost in their overuse and the trail of citations that vaguely lead to the original manuscripts. To help restore some organization, models were sorted into three categories based primarily on their mathematical and theoretical basis: (1) mass continuity-based, (2) nucleation-based, and (3) particle ensembles. This blog provides a concise catalogue of models and in most cases complete mathematical derivations. Furthermore, classes of models are unified by linking them to their theoretical origins, thereby making their derivations and physical interpretations more transparent. Each model has its own page wherein the derivations are presented along with an applet that illustrates how the model fits experimental data.

Beta versions of our applets for your consideration and use are posted; these are subdivided into three categories and can be found on the following pages:

Mass Continuity-Based Models

Nucleation-Based Models

Particle Size Distribution Models

Rheology Models

Very little commentary is provided on these pages, however, more detailed reviews are in the process of being published at this time.  These pages are posted for your use.  We encourage you to review the derivations carefully and to questions the results critically.

Please visit the site frequently, since other model applets will be posted as they are developed and existing applets revised as we receive your input.

J. J. Biernacki, Professor, Department of Chemical Engineering, Tennessee Technological University, Cookeville, TN 38505

List of Contributors

Tiantian Xie, PhD, Tennessee Technological University, May 2010

Benjamin Nation, Tennessee Technological University, Undergraduate Research Student (2009-2010)

About the Applets

The applets are Maple worksheets made web-accessible via MapleNet.  This process calls on Java, a programming language that enables you to talk to many web-based applications, including those using MapleNet.  You will need to have an updated version, at least Version 6 Update 20, to be sure that all of the applet features will work.  If you are using the Internet, you are likely already using Java, it’s free and easy ot access if you do not have it.  Go to the following website if you would like to or need to update your Java:

Bibliography of Related Publications


This site was made possible in-part by funding from the National Science Foundation (NSF) under Grant Nos. 0510854, 0757284 and CMMI-1563173. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

[1] T. Xie and J. J. Biernacki, The Origins and Evolution of Cement Hydration Models, Comp. Concr., 8(6), 647-675 (2011).

[2] J. J. Biernacki and T. Xie, An Advanced Single Particle Model for C3S and Alite Hydration, J. Am. Cer. Soc.,94(7), 2037-2047 (2011).

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